[EM] Tree based Condorcet strategies

[Juho]

Here's one basic example on how tree based Condorcet methods might  
work in practice.

Sincere preferences:
40: A
35: B>C
25: C>B

B would win (Condorcet winner).

Strategic votes:
40: A
35: B>C
25: C>A (strategic)

C would win.

When looking at the sincere preferences we see that B and C are  
clones. All B supporters think that C is the second best candidate.  
All C supporters think that B is the second best candidate. They look  
like coming from the same party or same bigger grouping (e.g. right  
wing).

It seems that it would be natural for the B and C "parties" to form  
an alliance. Together they will get 60% of all votes. All B and C  
supporters think that the alliance is ok since it will be made with  
the second best "party". All of them think that A should not win.

If B and C form an alliance (tree branch) the candidate tree will  
look like (A (B C)). At the top level the election will be a race  
between the (B C) branch and candidate A. Branch (B C) will win 60-40  
(even if C supporters would use the now useless strategy). Within  
that branch B has more support than C (even if C supporters would use  
the now useless strategy), so B wins.

Forming the alliance stripped away the possibility of C supporters  
burying B. Even if C supporters were planning to do so they maybe  
would agree to form the alliance if asked (otherwise their plans  
could become obvious, and B could e.g. seek for a deal with A).

The end result is very fair from the sincere preferences perspective.  
The alliance was quite natural. And it led to elimination of a risk  
of strategic voting.

So, at least in some cases tree based Condorcet methods seem to bring  
happiness to the world :-).

Juho




		
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